World formula

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A world formula or a theory of everything ( English theory of everything , ToE or TOE ) is a hypothetical theory , formed from theoretical physics and mathematics , which should precisely describe and link all physical phenomena in the known universe . Over time, the term has flowed into the popularization of elementary particle physics . In this research area, a world formula, i.e. a single, all-encompassing model, would explain and bring together the theories of all fundamental interactions in nature.

expectations

A theory of everything should, among other things , precisely describe all four basic forces - gravitation , electromagnetism and the weak and strong nuclear forces . One also speaks of a unification of forces or interactions.

The possible unification of the three basic forces, i.e. H. the electromagnetic, weak (unified in the electro weak calibration theory ), and the strong interaction ( Quantum ) without gravity, is as large unified theory designated ( Grand Unified Theory , GUT ). The possibility of this partial unification of the three gauge interactions is assumed due to the similarity in the mathematical structure of the three theories.

For the theory of everything, the inclusion of gravitation is particularly necessary. It is expected that this takes place at an energy of about 10 19 GeV (the Planck energy ), because an extrapolation of the interaction strength of the individual basic forces to this energy indicates that they are then all comparable, and because the Planck energy is gravitation and quantum field theory must be applied simultaneously in each case.

For example, a theory of everything should:

  • contain general relativity and quantum field theory,
  • explain the observed forces and particles of the Standard Model of elementary particles ,
  • explain the masses, coupling constants and mixing angles of the standard model of elementary particles ,
  • Describe the standard model of cosmology , as well as clarify and predict the processes in the early or late universe - especially the asymptotic behavior on very small or very large space and time scales,
  • clarify the nature of dark matter and dark energy ,
  • contain a consistent, renormalizable quantum theory of gravity, along with the description or avoidance of singularities.

Assumed features:

  • Supersymmetrical , uniform basic structure that goes beyond the traditional division into bosonic and fermionic degrees of freedom;
  • Physical degrees of freedom that go beyond four-dimensional space-time.

It is not clear whether a theory of everything predicts new particles or even new forces. Such new particles could be detectable with cosmological observations. The experiments at the Large Hadron Collider , which began at CERN in 2010 , were expected to make progress towards a world formula. However, this expectation has not been confirmed so far (mid-2020): no deviations from the standard model were found, no signs of a great unification of the three gauge interactions, no effects of supersymmetry, and no additional dimensions or degrees of freedom.

Many physicists are convinced that all physical processes can be traced back to a basic principle ( reductionism ) or at least can be described with a few consistent basic terms.

World formulas in history

Attempts to trace physical reality back to a single principle go back to antiquity. In ancient Greece, pre-Socratic philosophers speculated that the apparent variety of phenomena observed was due to a single type of interaction, namely the motions and collisions of atoms . The term "atom" introduced by Democritus was an early philosophical attempt to unify all phenomena observed in nature. Archimedes was possibly the first scientist to describe nature with axioms (or principles) and derive new results from them. So he tried to describe “everything” on the basis of a few axioms. Every theory of everything is expected to rely on axioms and derive all observable phenomena from them.

Based on Democrit's atomism , the mechanical philosophy of the 17th century assumed that all forces could ultimately be reduced to contact forces between the atoms, which were imagined as tiny solid particles. In the late 17th century, Isaac Newton's description of the action of gravity at a distance suggested that not all forces in nature result from mechanical contact with matter. In his Philosophiae Naturalis Principia Mathematica , Newton unified Galileo's work on gravity, Kepler's laws of planetary motion, and the phenomenon of tides by explaining these seemingly different phenomena in a single law: Newton's law of gravitation .

On the basis of these results, Laplace suggested in 1814 that a sufficiently powerful intellect would be able to calculate and determine every past and every future state with knowledge of all natural laws and all initial conditions such as the position, position and speed of all physical particles in the cosmos. This concept is also called the Laplace demon . So Laplace saw a theory of everything in a combination of gravitation and mechanics . Modern quantum mechanics , however, implies that the states of particles are not determined but are subject to probabilities, which is why Laplace's vision has to be changed: a theory of everything must contain gravitation and quantum mechanics.

In 1820, Hans Christian Ørsted discovered a connection between electricity and magnetism, thus triggering decades of work that culminated in James Clerk Maxwell's theory of electromagnetism in 1865 . In the 19th and early 20th centuries it gradually became clear that many common examples of forces - contact forces, elasticity, viscosity, friction, and pressure - result from electrical interactions between the smallest particles of matter. In his experiments from 1849–50, Michael Faraday was the first to look for a union of gravity with electricity and magnetism. However, he found no connection.

Emil du Bois-Reymond coined the German term “Weltformel” as early as 1872 in his speech “On the Limits of Knowledge of Nature” in the sense of a complete mathematical description of the world that, in his opinion, could not be realized. This designation is considerably older than the English equivalent "theory of everything".

In 1900, David Hilbert published a famous list of math problems . In Hilbert's sixth problem, he asked for an axiomatic basis for all physics to be found. So in this problem he asked what would be called a theory of everything today.

In the late 1920s, new quantum mechanics showed that the chemical bonds between atoms are examples of (quantum) electrical forces, leading Paul Dirac to say that “the underlying physical laws that govern the mathematical theory of a large part of physics and the whole of chemistry are necessary, thus are completely known "(in the original:" the underlying physical laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are thus completely known. ").

After Albert Einstein published his general theory of relativity in 1915 , the search for a unified field theory that would combine gravitation and electromagnetism began. At that time the strong and weak interactions had not yet been discovered. This began his more than thirty-year search for the so-called Unified Field Theory , which was supposed to show that gravitation and electromagnetism are manifestations of a single basic principle. An early theory that unified electromagnetic interaction and gravity was the Kaluza-Klein theory . However, it arose before the weak and strong interactions were known and was therefore incomplete. Albert Einstein tried until the end of his life to find a unifying theory, but was ultimately unsuccessful.

In 1958 Werner Heisenberg presented a formula that he called the equation of matter and whose main element was a massless original particle Psi (Ψ), from which all observable particles would later be composed. The press quickly hailed this equation as the universal formula , but criticism soon arose and colleagues discovered inconsistencies in the equation. Since these attempts, sometimes prematurely and exaggeratedly acclaimed in the press, the term universal formula has also been used in a derogatory, derisive sense for similar projects. In his quantum theory of the original alternatives, Heisenberg's student Carl Friedrich von Weizsäcker strived for a uniform description of nature based solely on quantum theory, which he understood in this context as a theory of information in time.

During the 20th century, the quest for a unifying theory was complicated by the discovery of the strong and weak nuclear forces (or interactions) that differ from both gravity and electromagnetism. Another hurdle was the assumption that quantum mechanics had to be included in such a theory from the beginning, instead of appearing as a result of a deterministic world formula, as Einstein hoped.

Gravitation and electromagnetism could always coexist as classical forces, but for many years it seemed that gravitation could not even be integrated into the quantum framework, let alone be united with the other fundamental forces. Because of this, for much of the twentieth century work on the Association focused on understanding the three "quantum forces": electromagnetism and the weak and strong interaction. The first two were combined in 1967-68 by Sheldon Glashow , Steven Weinberg and Abdus Salam to form the electroweak interaction . The electroweak union is a broken symmetry: the electromagnetic and weak forces appear different at low energies, because the particles that carry the weak force, the W and Z bosons, have a mass of 80.4 GeV / c² and 91.2 GeV / c², while the photon that carries the electromagnetic force is massless. At higher energies, W and Z bosons can be easily generated and the uniformity of force becomes clear.

Although the strong and electroweak forces peacefully coexist in the Standard Model of Particle Physics , they remain different. The search for a theory of everything has thus remained unsuccessful on two points: Neither has the strong and electroweak forces been combined in a large, unified theory, nor has these forces been combined with gravitation.

Two of the currently most popular theories for a uniform description of the four basic forces and for a quantum theoretical description of gravity are string theory and loop quantum gravity , whereby representatives of both theories emphasize that the existing theories are incomplete and that essential problems have still been solved in order to formulate a final theory Need to become. While string theory describes the fundamental building blocks that make up the world as vibrating one-dimensional or higher-dimensional objects, loop quantum gravity tries to quantize spacetime itself .

Unification steps

Theories that were previously seen separately have been or are currently being merged, as the following table shows:

Fundamental interactions and their descriptions
Strong interaction Electromagnetic interaction Weak interaction Gravity
classic Electrostatics & magnetostatics ,
electrodynamics 		Newton's law of gravitation ,
general relativity
quantum
theory 		Quantum
( standard model ) 		Quantum electrodynamics Fermi theory Quantum gravity  ?
Electroweak Interaction
( Standard Model )
Big Unified Theory  ?
World formula ("theory of everything")?
Theories at an early stage of development are grayed out.

term

The term universal formula contains a consistent or unambiguous description and prediction of the phenomena observable in nature within the framework of a simple set of mathematical formulas . The world formula is accordingly understood as a contrast to the current state of physics, in which one comes with different theories in different areas to predictions that do not contradict each other in practice, but obviously cannot be unified. This is currently being solved in such a way that, depending on the context, that theory is used which, based on experience, provides the greatest agreement with the respective experiment . In the border areas between the existing theories or their areas of validity , this inevitably results in decision conflicts and more or less large deviations from the experiments. One example of how such conflicts can be resolved for specific individual cases is Hawking radiation and the related Unruh effect .

In principle, the concept of the universal formula only refers to (in principle) measurable quantities in physics. In addition, the best current theories come with increasing complexity of the considered system to practical limits of predictability . However, this is not a restriction of the comprehensive explanatory claim of these theories in their respective areas of validity.

So it is e.g. For example, even today it is not even possible to describe a human organism using quantum electrodynamics (QED), because the number of matter particles it contains by far exceeds the storage capacity of current computers . Nevertheless, physics has a very high degree of confidence in the validity of quantum electrodynamics in this problem area, since its application to all practically solvable problems investigated so far has shown an extremely good agreement with the experiments. Thus, one also assumes that composite, but no longer practically solvable systems of QED will show this degree of agreement. In exactly the same sense, a future TOE will therefore lay claim to the explanation of all measurable natural phenomena.

The term universal formula is not only to be understood in the figurative sense. A physical theory of everything will probably not be reduced to a single mathematical formula , but rather be based on a system of coupled superordinate differential equations. Instead of a world formula, a mathematical world equation system is required, which contains physics as a special solution.

Every physical theory of a certain aspect of the world contains, in addition to the equations that support it, many other explanatory elements, without which it cannot be applied. These include, above all, the regulations on how the quantities occurring in the equations are to be measured. A system of world equations must be independent of regulations.

The world formula is also expected to describe the beginning of our universe ( big bang theory ) and thus the creation of space, time, mass and energy.

criticism

The concept of a theory of everything is at the center of an internal scientific debate about reductionism . Some scholars, including Robert B. Laughlin and Philip Warren Anderson , deny the fundamental possibility of explaining complex facts with such a theory, criticize what they consider to be the disproportionate research funds that are raised for the search for the world formula, and present the concepts to it of emergence and self-organization opposed.

Cultural processing

In numerous novels, films and plays, a world formula that has been found but not yet public plays a role. A well-known example is the comedy Die Physiker by Friedrich Dürrenmatt .

See also

literature

Web links

Individual evidence

  1. ↑ SWR2 Knowledge (Aula July 6, 2008): Inside the World (rtf; 38 kB) .
  2. ↑ Chris Impey: How It Began: A Time-Traveler's Guide to the Universe . WW Norton, New York and London 2012, ISBN 978-0-393-08002-5 . P. 340
  3. ↑ Michael Faraday : Experimental Researches in Electricity. Twenty-Fourth Series. On the Possible Relation of Gravity to Electricity . Abstracts of the Papers Communicated to the Royal Society of London, London 1850, doi : 10.1098 / rspl.1843.0267 . P. 994 f.
  4. ^ Emil du Bois-Reymond : About the limits of the knowledge of nature. A lecture at the second public session of the 45th Assembly of German Naturalists and Doctors . von Veit & Co., Leipzig 1872. p. 4 ff.
  5. ^ Paul Dirac : Quantum mechanics of many-electron systems . Proceedings of the Royal Society of London A, London 1929, doi : 10.1098 / rspa.1929.0094 . P. 714
  6. ↑ Christopher Schrader: Heisenbergs Weltformel Spektrum.de (2018).
  7. ↑ Alexander Blum: Heisenberg and the search for a definitive theory Max Planck Institute for the History of Science (2018)
  8. ↑ The objection of Peter Woit is well known , who wants to classify the string theory as "not verifiable" with the formulation Not even wrong .
  9. ↑ Robert B. Laughlin and David Pines : "The Theory of Everything" , Proceedings of the National Academy of Sciences ( PNAS ) 97, 28-31. online@pnas.org Retrieved May 28, 2011.
  10. ↑ Robert B. Laughlin : Farewell to the universal formula: The reinvention of physics . 4th edition. Piper Verlag, Munich 2007, ISBN 978-3-492-04718-0 .